F=BsplineFunction[model]; "Model surface as B spline Function"
SurfaceSampling[p_] := Flatten[Table[F[u, v], {u, 0, 1, p}, {v, 0, 1, p}], 1]; "Surface Sampling Function"
ModelSurface= SurfaceSampling[0.005]; "Actual sampling"
g=Drop[T1[[2]][[1]].Append[vec,1],-1] "T1 Geometric Transform of point "vec""

T1=FindGeometricTransform[Nearest[CtrlPts, ModelSurface],CtrlPts,"Transformation"->"Rigid",Method->"FindFit"]; "CtrlPts is the point could"

ModelSurface = Map[g,ModelSurface] "Apply found transformation to the ModelSurface"
 T = T1[[2]][[1]].T; "After some iteration, T will become the optimal trasformation"